Bernie,
The 17 Remy, and the 17 caliber wildcats that mimic its ballistics are the quintessential 17's for coyotes and easily the best go to 17 when the ranges get long. All of them are DRT on coyotes with a good hit. The 17 Remy is always at its best with worked up handloads, and that is especially true in the short tubes to get the best efficiency out of it. The 17MachIV didn't replace the 17 Remy, so IMO the newer 17 Rem Fireball will not either. While the 17M4 (and so the 17 RFB) are also excellent coyote choices that are effective almost as far as the 17 Remy, they are just not as decisive on the longer shots or on shots that don't quite find the mark you had hoped they would. If you decide to keep the 17 Remy barrel you really need to load for it though. Way easier now days than when I got my first one. I still have my form/trim/ream dies to take 223 brass down to it, a well over $300 die set - ouch! Picking up 17 brass is now easy enough, plus you have the factory ammo brass you could reload and they may be more than enough for your uses (if not I've got a bunch). The brass will last a long time and give you many firings, especially if not pushed to max. The 17HMR will get it done too at your ranges with shot placement. Enjoy that barrel pard - its a keeper.
Larry